A350575 Squarefree numbers k such that k + (k reversed) is also squarefree.

1, 3, 5, 7, 10, 11, 14, 15, 19, 21, 23, 30, 33, 34, 37, 41, 42, 43, 46, 51, 55, 58, 59, 61, 67, 69, 70, 73, 77, 78, 82, 85, 86, 87, 89, 91, 94, 95, 101, 102, 105, 106, 109, 111, 115, 118, 119, 130, 131, 134, 138, 139, 141, 142, 146, 149, 151, 155, 158, 159, 161, 166, 170, 174, 178, 181, 182, 185, 190, 191, 194, 195, 199

Offset: 1

Author

Jean-François Alcover, Jan 07 2022

Keywords

• nonn
• base
• easy

Comments

This is to squarefree numbers what A061783 is to primes.

Examples

			14 is a term since it's squarefree and so is 14 + 41 = 55.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004086, A005117, A056964, A061783.

Programs

Maple

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
q:= n-> andmap(numtheory[issqrfree], [n, n+R(n)]):
select(q, [$1..200])[];  # Alois P. Heinz, Jan 07 2022

Mathematica

okQ[n_] := SquareFreeQ[n] && SquareFreeQ[n + IntegerReverse[n]];
Select[Range[200], okQ]

PARI

isok(m) = issquarefree(m) && issquarefree(m+fromdigits(Vecrev(digits(m)))); \\ Michel Marcus, Jan 07 2022

Python

from sympy.ntheory.factor_ import core
def squarefree(n): return core(n, 2) == n
def ok(n): return squarefree(n) and squarefree(n + int(str(n)[::-1]))
print([k for k in range(1, 200) if ok(k)]) # Michael S. Branicky, Jan 07 2022